Contradiction with Kirchhoff's Radiation Law?

[eat_2_much]

Hello everyone,

I am working on understanding how Kirchhoff's Radiation Law applies in the real world. Basically, the absorbed solar radiation must equal the thermal radiation if a surface is to be at equilibrium. Certain relationships follow from this assumption, namely, for an opaque material, absorptance is equal to emissivity coefficient.

Here is the problem I am having. If I look up radiation properties for different materials, I can find an absorptance coefficient and an emissivity coefficient and they are not equal. Why does this occur? This seems to contradict Kirchhoff's law! I have included a couple of links for an example of what I am talking about.

http://www.solarmirror.com/fom/fom-serve/cache/43.html
https://books.google.com/books?id=X...nepage&q=absorptance emissivity table&f=false

Can anyone resolve this contradiction for me?

 

[Khashishi]

It's because the spectrum of sunlight is different from the spectrum of the thermal radiation. For any given wavelength, the emissivity and absorption must be equal.

 

[Andy Resnick]

Here is the problem I am having. If I look up radiation properties for different materials, I can find an absorptance coefficient and an emissivity coefficient and they are not equal. Why does this occur? This seems to contradict Kirchhoff's law! I have included a couple of links for an example of what I am talking about.

http://www.solarmirror.com/fom/fom-serve/cache/43.html
https://books.google.com/books?id=Xn8KbsgeFrwC&pg=PA212&lpg=PA212&dq=absorptance+emissivity+table&source=bl&ots=Rm1mGpnfmB&sig=kLvSUxBKTntrP26lvc8j9CWaoiM&hl=en&sa=X&ved=0ahUKEwjP2-bp5vHRAhXBqFQKHeVHDFcQ6AEILjAD#v=onepage&q=absorptance emissivity table&f=false

Can anyone resolve this contradiction for me?

There are two important points- 1) the reported numbers are band-averages, and it's not clear if the waveband used for solar absorption is the same as used to report emissivity, and 2) rough surfaces often have angle-dependent absorption and reflection, and it is not clear if the absorption and emissivity values are angle-averaged.

Some of point #1 is addressed both in the CRC text and in the mirrored URL http://www.redrok.com/concept.htm#emissivity

The second point is a little more tricky than the first: for example, the solar absorption can mean normal incidence, but the emissivity means 'emitted into the full hemisphere'.

Does this help?

 

[eat_2_much]

Andy - I understand what you are saying! Your post was helpful - Thanks!

To make sure I understand Khashishi correctly - The emissivity coefficient only applies for the thermal radiation spectrum; however, sunlight consists of other wavelengths of radiation - not just thermal radiation. Absorpstance values can be a average over the entire sunlight spectrum while the emissivity coefficient is just governing the thermal radiation spectrum. This can create absorpstance and emissivity coefficients that are not equal.

Does this seem reasonable? At least it represents one reason among the several given here why the values could be different.

 

[Khashishi]

Basically, Andy's first point covers the same thing as I was saying. Presumably, the terrestrial object is at a much lower temperature than the Sun, so you are comparing the absorptivity for visible light to the emissivity for infrared light. Not the same thing.